Two charges, +Q and ‑Q, are located two meters apart and there is a point along the line that is equidistant from the two charges as indicated. Which vector best represents the direction of the electric field at that point?
a. Vector EA
b. Vector EB
C. Vector EC
d. The electric field at that point is zero.
please explain your answer thanks!
Electric field points in the direction that a positive charge will move.
To determine the direction of the electric field at the point, we need to consider the interaction between the two charges (+Q and ‑Q).
The electric field is a vector quantity that points in the direction of the force that would be exerted on a positive test charge placed at that point.
In this case, since the charges have opposite signs, the electric field lines will point away from the positive charge (+Q) and towards the negative charge (-Q).
At a point equidistant from the two charges, the electric fields due to the charges will be equal in magnitude but opposite in direction. This means that the electric fields will cancel out each other at that point, resulting in a net electric field of zero (d).
Therefore, the correct answer is d. The electric field at that point is zero.
To determine the direction of the electric field at the point equidistant from the two charges, we can make use of the principle that the electric field created by a positive charge points away from it, while the electric field created by a negative charge points towards it.
In this scenario, we have two charges, +Q and -Q, located two meters apart. The point of interest is equidistant from the two charges, which means it is in the middle of the two charges.
Let's analyze the electric fields created by the two charges separately:
1. Electric Field created by the positive charge (+Q):
The electric field created by a positive charge always points away from the charge. Therefore, the electric field created by the +Q charge at the point of interest will point away from it.
2. Electric Field created by the negative charge (-Q):
The electric field created by a negative charge always points towards the charge. Therefore, the electric field created by the -Q charge at the point of interest will point towards it.
Since the point of interest is located in between the two charges, the electric fields created by the charges will have different directions. The electric field created by the +Q charge points away from it, while the electric field created by the -Q charge points towards it.
To find the net electric field at the point of interest, we need to consider the vector sum of the electric field vectors created by the charges. The vector sum can be obtained by adding the magnitudes of the two vectors and assigning the resultant vector the same direction as the larger magnitude vector.
In this case, since the +Q charge and -Q charge are of the same magnitude, the magnitudes of the electric fields created by them will also be equal. Therefore, the electric field vectors will be of equal magnitude.
Now, let's evaluate the options:
a. Vector EA: Represents the electric field created by the +Q charge. It points away from the +Q charge.
b. Vector EB: Represents the electric field created by the -Q charge. It points towards the -Q charge.
c. Vector EC: Since the magnitudes of the electric fields created by the +Q and -Q charges are equal and opposite, the resultant electric field vector will be zero at this point. Therefore, the correct answer is vector EC.
d. The electric field at that point is zero: This option is not correct because, as explained above, the electric fields created by the +Q and -Q charges do not cancel out completely. They have equal magnitude but opposite directions, resulting in a non-zero net electric field.
Therefore, the correct answer is c. Vector EC, as it represents the direction of the electric field at the point equidistant from the two charges.